All of the H&R Block shares that investors own are worth $9.1 billion, making the four-year buyback plan equal to nearly 40 percent of the company’s current total value. An increase in Block’s share price would increase the company’s total value.

Companies buy back their shares as a way to support the value of the shares that remain in investors’ hands. They serve in effect as an additional big buyer in the marketplace.

The Kansas City-based tax preparation company said it will launch the buyback Wednesday with a monthlong “modified Dutch auction” tender offer. The offer would buy back up to $1.5 billion worth of its shares.

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With the type of auction Block announced, it will buy shares at between $32.25 a share and $37 a share. More details are to be announced Wednesday morning.

Shares of H&R Block closed at $32.95, down $1.07, or 3.15 percent, before the company’s announcement.

Block also said Tuesday it completed the long-awaited sale of the H&R Block Bank to BofI Federal Bank a month ahead of schedule. The bank sale freed Block from federal regulation as a bank holding company, which had forced it to keep more capital on hand than it otherwise needed.

“We have a long tradition of returning capital to shareholders, and I’m pleased that we can now continue that tradition,” Block chairman Bob Gerard said in the company’s capital plan announcement.

Last month, Block said it had won regulatory approval to sell the bank to BofI. It had been trying to win federal approval of a sale since July 2013.

As a retail tax preparation business, Block can operate as a “capital light” company, chief financial officer Greg Macfarlane said during a conference call with analysts.

The stock buyback is part of a broader new capital plan for the company in which Block will take on more debt. The move would tend to increase the return for shareholders by leveraging their investment with the borrowed funds.

Macfarlane said he expects Block’s additional debt would allow it to maintain its investment grade status with rating agencies Standard & Poor’s and Moody’s Investors Service.

Cobb told analysts that selling the bank also had completed the company’s long journey away from previous efforts to expand beyond taxes. These include exits from the subprime mortgage lending, stock brokerage and accounting businesses, among others.

“We now have the company we wanted,” Cobb said. “We’ve got a nice simple story now that I’m proud of.”

Block announced the plans after reporting it had narrowed its normal first-quarter loss with a bump up in revenue.

The company said it lost $99.7 million, or 36 cents a share, in the three months since tax season ended. A year ago, its losses totaled $116.2 million, or 42 cents a share.

Revenue in the quarter totaled $137.7 million, compared with $133.6 million a year ago.

The new report covers May, June and July, the first quarter of Block’s fiscal year, which ends each April 30 after tax season. Block historically loses money in the quarter, when revenue is low because tax activity among consumers is especially low.